Implementation of a space-time formulation for incompressible flows in the particle finite element method context

• Grant number: 23/01688-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 20, 2023
• End date: February 15, 2024
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Rodolfo André Kuche Sanches
• Grantee: Darcy Hannah Falcão Rangel Moreira
• Supervisor: Sergio Idelsohn Barg
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: International Centre for Numerical Methods in Engineering (CIMNE), Spain
• Associated to the scholarship: 21/07516-9 - Three-dimensional numerical analysis of fluid-structure interaction with structural contact, BP.DR

Abstract

This proposal aims at the development of a space-time formulation of the finite element method based on particle position (PFEM). The essence of this approach is the treatment of time as a dimension ofproblem, which leads to space-time discretizations. Space-time formulations have the potential to allow different space meshes within a time interval, eliminating the need for data projection during remeshing, what makes easier the treatment of flows with topological change of the fluid domain. On the other hand, PFEM represents the fluid domain by a cloud of moving particles that carry the flow properties, and a finite-element mesh is generate each time step, taking the particles as nodes, to evaluate the particle interaction forces. Due to the continuous remesh, PFEM naturally handles problems with large distortions and topological changes. In this way, combine space-time formulation to PFEM can lead to a more robust and precise technique to be applied to the simulation of fluid-structure interaction problems with topological changes. (AU)